In a conventional radio system utilizing a digital or analog phase modulation scheme, the phase of the received signal can be extracted using zero-crossing information. Specifically, the received signal at an intermediate frequency (IF) is applied as an input to a voltage limiter. Next, the system transforms the output of the voltage limiter into digitally encoded phase information. One way to digitize the limited received signal is to sample the signal at the zero-crossing levels. Typically, the system samples the voltage limited received signal at either the positive or the negative zero-crossings levels. FIG. 6 illustrates a received signal 701 and a voltage limited signal 705. A voltage limiter has an internal voltage threshold V.sub.t 703. The output signal of the voltage limiter is specified by the following input-output characteristic EQU V.sub.h if V.sub.in &gt;V.sub.t EQU V.sub.out = EQU V.sub.L if V.sub.in &lt;V.sub.t
where V.sub.h and V.sub.L are the high and low logic levels, respectively. For an ideal limiter Vt is equal to zero. However, ideal voltage limiters are difficult to manufacture in large volumes due to differences in make tolerance and the variation of the part over temperature. When the voltage threshold V.sub.t is not equal to zero, the positive and negative zero-crossings will not be exactly 180 degrees out of phase, and the limiter output signal becomes asymmetric. The asymmetry causes a discrepancy in the phase at the positive zero-crossings relative to the phase at the negative zero-crossings. As illustrated in FIG. 6, the time T1 707 is less than time T2 709. In a system using positive and negative zero-crossings to sample the phase of the received signal, the difference in time results in distorted phase information. Most conventional systems resolve this problem by sampling only at the positive zero-crossings of the voltage limited signal. However, it is a desirable feature of a phase demodulating system to be able to sample at both the positive and negative zero-crossings. By doing so, the phase quantization portion of the system can operate at one-half the frequency typically required to extract phase information.
To quantify the discrepancy in phases at the positive and negative zero-crossings, the received intermediate frequency signal can be represented as EQU s(t)=A(t)sin[2.pi.fi t+.theta.(t)]
where .theta.(t) is the phase modulation to be recovered. At the IF zero-crossings s(t) will be zero, and the phase signal .theta.(t) can be represented as EQU .theta..sub.+ (t)=[-2.pi.f.sub.i t.sub.k +asin(V.sub.t /A(t))].sub.mod 2.pi. at positive zero-crossings EQU .theta..sub.- (t)=[-2.pi.f.sub.i t.sub.k +.pi.-asin(V.sub.t /A(t))].sub.mod 2.pi. at negative zero-crossings.
When the phase modulation is constant, .theta..sub.+ (t) and .theta..sub.- (t) should differ by exactly .pi. radians; however, a non-zero limiter threshold V.sub.t results in an average phase error term equal to EQU .epsilon.=E{.theta..sub.+ (t)-.theta..sub.- (t)+.pi.}=2asin[V.sub.t /A(t)]
To compensate for the deleterious effects of asymmetric limiting, this phase error term must be removed.
The implementation of phase demodulator systems which sample at both positive and negative zero-crossings allows a reduction of the intermediate and reference oscillator frequencies by one-half. The result is a decrease in current drain, which translates into extended battery life in a portable product. Therefore, it would be advantageous to develop a method of digitally compensating for voltage limiter asymmetries.